# The base edges of two square pyramids are in the ratio 1 : 2 and their heights in the ratio 1 : 3. The volume of the first is 180 cubic centimeters. What is the volume of the second?

Let the volume of first pyramid be V1

Let the base edge of first pyramid be a1

Let the height of first pyramid be h1

Let the volume of second pyramid be V2

Let the area of first pyramid be a2

Let the height of first pyramid be h2

We know that,

Volume of a pyramid

Volume of a first pyramid …..(1)

Volume of a second pyramid …(2)

Given:

a2 = 2a1 …(a)

Given:

h2 = 3h1 …(b)

Consider, Volume of a second pyramid

(from a and b)

V2 = 12×V1

V2 = 12×180 = 2160cm3

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